AP EAMCET · Maths · Straight Lines
If \(M\) is a point on the line \(y=x\) and points \(P(0,1), Q(2,0)\) are such that \(P M+Q M\) is minimum, the coordinates of \(M\) are
- A \((0,0)\)
- B \(\left(\frac{13}{17}, \frac{13}{17}\right)\)
- C \(\left(\frac{2}{3}, \frac{2}{3}\right)\)
- D \(\left(\frac{31}{7}, \frac{31}{7}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{2}{3}, \frac{2}{3}\right)\)
Step-by-step Solution
Detailed explanation
Given, \[ \begin{aligned} & P=(0,1) \\ & Q=(2,0) \end{aligned} \] Let \(\quad M=(a, a) \quad[\because M\) lies on the line \(y=x]\) In order to Make \(P M+Q M\) is minimum \(\Rightarrow P, M, Q\) Must be collinear \(\therefore\) Slope of \(P M=\) Slope of \(Q M\)…
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